TranscriptSolving Multi-Step Inequalities

Rocky is watching television while eating his favorite food, meatballs, when suddenly...This could be the perfect opportunity for Rocky's great comeback. To figure out how he can get back into shape, we can use solving multi-step inequalities. He remembers the good 'ol days when he was fit and won the beauty contest. He has to get in shape in ten days. This requires a call to his former coach.

Rocky won competitions at a weight of 50 pounds. He knows from his old workout schedule that he loses five pounds during a workout session. He has gained a lot of weight and now weighs seventy pounds. Therefore, he has to lose twenty pounds in ten days to reach his former weight. But, he loves his meatballs and has to eat meatballs daily, so he still gains two pounds a day in meatball weight.

The minimum

We want to know the minimum number of workout sessions Rocky needs to lose twenty or more pounds. Let's look at the facts: he loses five pounds each session. Let's let x stand for the number of workout sessions. Rocky gains two pounds a day for 10 days. In the end, he wants to lose 20 or more pounds. So we put an equal to or less than sign in between.

multiplying and subtracting

Simplify the value inside of the parenthesis by multiplying. Then, collect like terms. Apply the opposite operation to move the twenty to the right side of the inequality. This can be accomplished by subtracting twenty on both sides of the inequality. Now we can solve for x. Again, apply the opposite operation to eliminate the negative five in front of the x. This can be accomplished by dividing both sides of the inequality by negative five.

Be careful: The inequality sign is reversed each time we divide by a negative number. The result is X is greater than or equal to eight. So, he starts training. Now that Rocky has had eight training sessions, let's check on his progress. Substitute X in the equation with the number eight. Simplify the left side of the inequality by multiplying.

solve the Multi-Step inequality

Then, complete the addition on the left side of the inequality. If Rocky has eight training sessions, he will definitely reach his goal! But what if he trains more than that? Rocky has two more training sessions. To see what happens when Rocky has more training sessions, we can substitute X with ten - or any other number greater than 8.

As you can see, we get a true statement again, so if Rocky trains for more than 8 sessions, he will also reach his goal. Woohoo! Rocky won the competition! Let's have a look at his prize. His prize is meatballs for a lifetime. Poor Rocky, will he ever win another competition? Luckily, he still has his coach.

About this Video Lesson

Description

Just like equations, inequality problems can require multiple steps to calculate the answer. The steps to solve multi-step inequality problems start out the same as the steps to solve multi-step equations.

First, if parentheses are used in the problem, simplify those terms. Use the Distributive Property if needed. Next step, collect the like terms by adding and subtracting. After that, solve for the variable using opposite operations. This all seems the same – but watch out. The difference is the inequality sign. Your last step in solving the problem is to attend to the inequality sign.

To solve for the variable, if you multiplied or divided by a negative number, you must flip the inequality sign, so it points in the opposite direction. In other words, if you multiply or divide by a negative number, greater than (>) becomes less than (